Why does hot air rise / why does a hot (hotter) molecule rise?

I was opening the freezer earlier thinking about all the cold air that rushes out when I open the door. I got to wondering if it came out so quickly because of the "suction action" of pulling on the freezer door (would opening the door slowly make a difference?) and I was wondering if the cold air just came falling out because of gravity (kindof like if the freezer was full of sand and I opened the door I'd expect the sand to fall out). But that got me to thinking that there's already air at a lower level than the freezer (warmer air, but still air none-the-less). So why should the cold air want to trade places with the warm air.

In my mind the mental model was similar to the trick of taking a can of mixed nuts and shaking it. The big brazil nuts tend to shake to the top of the can, and the little peanuts tend to shake to the bottom. If the big nuts could move to the bottom of the can they would, but they can't - there are too many little nuts in the way. This by itself doesn't explain anything other than in a statistical way saying it's easier for the big nuts to move upwards.

Anybody shaking a jar of sand with a rock in it sees the same thing - put the rock in the bottom of the jar - fill the jar with sand - shake it - and gradually the big rock moves to the top. It's not that gravity acts any differently on the big rock or on the grains of sand, but the big rock just has less opportunity to move downward because every time it moves - a smaller grain moves in under the big rock preventing downward movement. The only direction the big rock _can_ move is up. Similarly in my mind gravity should work on a hot and cold air molecule similarly - so it seems gravitational force should cancel. (put a hot and cold molecule in a vacuum and is there any tendency for one to move upward and the other downward? so it seems like this is more of an emergent statistical system dynamic at work where the "hot air rises/cool air sinks" tendency may come from.)

So in this model the big brazil nuts or the big rock represent the warmer air molecules, and the little nuts or the grains of sand represent the cooler air molecules. The warmer molecules have more energy and bounce around more - so they're creating more space around themselves - which when the opportunity presents itself - the cooler air from the freezer is perfectly happy to fill if given the chance. The warm air molecule might certainly try to bounce downward but is more likely to run into resistance that prevents it. The cooler molecules are less bouncy and have less energy - so its tougher for them to rise vs. gravity, and being less bouncy can also be closer together (like the sand or peanuts).

Ehhh. Anyway, that's how I was thinking of it. I looked up a google search and this discussion came up as the first search result.

It's a pretty interesting read. Discussion of bouyancy, gas densities, behaviors of gases in magnetic fields, and some other things. It still has the feel of "here's what happens and it can be explained what will happen," but the underlying why it happens as it does seems a little more amorphous to me. There's one post that actually says something along the lines of: "why aren't the energetic warmer particles as likely to move downward as upward?" I think maybe they do try to move downward, but they're less successful because that's where more cool particles are likely to be - because the cooler particles have less of a choice - the cooler air can't overcome gravity as well and is more statistically likely to be in the way.

If you take this scenario into space without gravity, and have 2 equal cannisters of same #molecules of a gas - and released it - I'd think youd end up with with an expanding sphere, with more warm particles farther from the center, and more cool air particles toward the center of the sphere.

I wonder if you tried the same experiment in space with mixed nuts or sand/rock, would the bigger nuts and bigger rocks end up farther out from the sphere with more smaller nuts/grain sands staying toward the inside of the sphere?